Question

Find the LCD of the given rational equation

Answer 1

Answer:

$=\frac{2x^3+x^2-11x+14}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}$

Step-by-step explanation:

Step 1: Factor $x² + 2x - 8: (x - 2) (x + 4)$

$=\frac{x}{x+4}+\frac{x-1}{x+2}+\frac{3}{\left(x-2\right)\left(x+4\right)}$

Step 2: Find the Least Common Multiplier of  $x + 4, x - 2, (x + 4), (x - 2)$

= $(x + 4) (x + 2) (x - 2)$

Step 3a: Conform the fractions based on the LCM (Least Common Multiplier)

= $\frac{x\left(x+2\right)\left(x-2\right)}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}+\frac{\left(x-1\right)\left(x+4\right)\left(x-2\right)}{\left(x+2\right)\left(x+4\right)\left(x-2\right)}+\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+4\right)\left(x+2\right)}$

Step 3b: The denominators are equal, so combine the fractions.

$=\frac{x\left(x+2\right)\left(x-2\right)+\left(x-1\right)\left(x+4\right)\left(x-2\right)+3\left(x+2\right)}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}$

Step 4: Expand $x(x + 2)(x - 2) +(x-1)(x+4)(x-2) + 3(x-2)$

$=\frac{2x^3+x^2-11x+14}{\left(x+4\right)\left(x+2\right)\left(x-2\right)}$

Have a great day!